A plane meets the coordinate axes at A,B,C such that the centroid of triangle ABC is (3,4,-6). Find the equation of the plane. The answer given in the book is:4x+3y-2z=36

Asked by Manoj | 20th May, 2013, 06:40: PM

Expert Answer:

A = (x,0,0); B = (0,y,0); C = (0,0,z)
Centeroid of the traingle ABC  (x+0+0/3, 0+y+0/3, 0+0+z/3) = (x/3, y/3, z/3)
hence, (3,4,-6) = (x/3, y/3, z/3)
x = 9, y = 12, z = -18
 
Hence, equation of plane = x/9 + y/12 + z/(-18) = 1
4x+3y-2z = 36

Answered by  | 21st May, 2013, 05:49: AM

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